1. Field of the Invention
The present invention pertains to the estimation of transmission velocities and more particularly to tomographic estimation of transmission velocities by first calculating raypaths and wavepaths from traveltime tables.
2. Related Prior Art
Prior art has illustrated ways of determining raypaths and wavepaths for the tomographic estimation of transmission velocities.
In one method, traveltimes have been generated synthetically from models containing isolated perturbations of velocities, which are then reconstructed tomographically. This method only shows the resolution at a single point. In a second method, raypaths are traced between source and receiver pairs for a particular velocity model by shooting or relaxation methods. Each raypath represents only an infinitesimal amount of energy and may behave pathologically in regions with strong velocity contrasts.
A cross-well, shear-wave data set posed two problems. First, wells are separated by only twelve and one half wavelengths, so thin raypaths are a poor approximation. Second, data are recorded through a high-velocity limestone surrounded by low-velocity shales. Waves are bent considerably, so either refracted or direct arrivals can arrive first. Only first-arrivals can be picked with any reliability.
Like velocity analysis, traveltime tomography estimates a velocity model that explains the arrival times and moveouts of coherent arrivals. Traveltime tomography is most sensitive to smooth background changes in transmission velocities, those changes which must be known for depth migration or diffraction tomography.
Current methods of seismic traveltime tomography use a variety of methods described as "ray-tracing" or "ray-shooting". These methods invoke Snell's law at boundaries of cells of constant velocity or dynamically extrapolate differential ray equations. Other alternatives include relaxation methods. Prior art has produced methods that constrain raypaths as a sum of low-order sinusoids and minimizes traveltimes with a simplex search algorithm. Other methods have been proposed applying perturbation theory directly to finite-difference extrapolations of the Eikonal equation.
All these methods assume asymptotically infinite frequencies in the source, and by implication, infinitely thin raypaths. However, frequency content can limit tomographic resolution more drastically than angular coverage. Recent methods have built on earlier methods to replace raypaths in tomography by "band-limited raypaths" or "wavepaths".
Examples of methods by which prior art has illustrated ways of estimating transmission velocities are as follows.
In the publication Numerical Recipes, Press et al, 1986, Cambridge Univ. Press, Chapter 16, "Two Point Boundary Value Problems", discusses numerical shooting and relaxation methods.
The publication by Society of Exploration Geophysicists expanded abstracts from the 1989 International Meeting and Exposition included an article titled "Efficient Seismic Ray Tracing Using Graph Theory" by T. J. Moser. This article discussed a method which proposed that the shortest path method is an efficient, accurate and flexible way to compute raypaths. Not only rays corresponding to first arrivals can be found, but also reflections on interfaces and other later arrivals. The method can be generalised and then applied to a much wider class of problems, like modeling of non-point sources, exploding reflectors and migration of traveltime data. Other graphtheoretical algorithms, like the second shortest path procedure and the reoptimisation of shortest paths, have practical applications in seismics.
Society of Exploration Geophysicists expanded abstracts from the 1989 International Meeting and Exposition, also included an article by John E. Vidale titled "Finite-Difference Calculation of Traveltimes in 3-D". This article stated that the travel times of first arriving seismic rays through most velocity structures can be rapidly computed on a three-dimensional numerical grid by finite-difference extrapolation. Head waves are properly treated and shadow zones are filled by the appropriate diffractions. Differences of less than 0.11 percent were found between the results of this technique and ray-tracing for a complex model. This scheme has proven useful for earthquake location, and shows promise as an inexpensive, well behaved substitute for ray-tracing in forward-modeling and Kirchhoff inversion applications.
U.S. Pat. No. 4,330,872, "Common-Offset-Distance Seismic Trace Filtering", issued to Robert H. Bratton, relates to a multiple coverage seismic exploration technique providing for a plurality of seismic trace recordings along a line of exploration. From these recordings, sets of common-offsetdistance traces are gathered. Initial estimates are made of the apparent dips associated with the seismic reflection signals across each set of common-offset-distance traces. These initial dip estimates are smoothed and the sets of common-offset-distance traces filtered along the apparent dips associated with the smoothed dip estimates to enhance the signal-to-noise ratio of the primary reflection signals.
U.S. Pat. No. 4,839,869, "Methods for Processing Converted Wave Seismic Data", issued to Chris T. Corcoran, relates to methods for processing converted wave seismic data which includes, fractional point gathering of the data in a manner consistent with a selected velocity model, dynamic correction of the data using parameters measured from the data to account for the asymmetric travel path of the converted wave rays and stacking the dynamically corrected data. Methods are also provided for updating the velocity model.